# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

May 2020 , Volume 16 , Issue 3

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2020, 16(3): 1037-1047 doi: 10.3934/jimo.2018191 +[Abstract](2397) +[HTML](1061) +[PDF](264.4KB)
Abstract:

This paper analyzes capital structure's characteristics and presents its simplified mathematical model. Panel data analysis shows that the listed companies prefer equity financing rather than debt financing. Furthermore, we propose a capital structure optimization model with uncertain equity financing constraints. We formulate the capital structure optimization problem as a two-stage stochastic optimization problem and solve it. Finally, numerical examples show that our optimization approach can improve the statistics result of capital structure adjustment.

2020, 16(3): 1049-1076 doi: 10.3934/jimo.2018192 +[Abstract](2117) +[HTML](903) +[PDF](786.28KB)
Abstract:

Two types of the law of iterated logarithm (LIL) and one functional LIL (FLIL) are established for the sojourn time process for a multiclass queueing model, having a priority service discipline, one server and $K$ customer classes, with each class characterized by a batch renewal arrival process and independent and identically distributed (i.i.d.) service times. The LIL and FLIL limits quantify the magnitude of asymptotic stochastic fluctuations of the sojourn time process compensated by its deterministic fluid limits in two forms: the numerical and functional. The LIL and FLIL limits are established in three cases: underloaded, critically loaded and overloaded, defined by the traffic intensity. We prove the results by a approach based on strong approximation, which approximates discrete performance processes with reflected Brownian motions. We conduct numerical examples to provide insights on these LIL results.

2020, 16(3): 1077-1098 doi: 10.3934/jimo.2018193 +[Abstract](3362) +[HTML](1220) +[PDF](458.65KB)
Abstract:

In Bitcoin system, a transaction is given a priority value according to its attributes such as the remittance amount and fee, and transactions with high priorities are likely to be confirmed faster than those with low priorities. In this paper, we analyze the transaction-confirmation time for Bitcoin system. We model the transaction-confirmation process as a queueing system with batch service, M/\begin{document}$\mbox{G}^B$\end{document}/1. We consider the joint distribution of numbers of transactions in system and the elapsed service time, deriving the mean transaction-confirmation time. Using the result, we derive the recursive formulae of mean transaction-confirmation times of an M/\begin{document}$\mbox{G}^B$\end{document}/1 queue with priority service discipline. In numerical examples, we show the effect of the maximum block size on the mean transaction-confirmation time, investigating the accuracy region of our queueing model. We also discuss how the increase in micropayments, which are likely to be given low priorities, affects the transaction-confirmation time.

2020, 16(3): 1099-1117 doi: 10.3934/jimo.2018194 +[Abstract](2141) +[HTML](991) +[PDF](443.8KB)
Abstract:

Peer-to-peer (P2P) networks have been commonly applied into many applications such as distributed storage, cloud computing and social networking. In P2P networks fairness fosters an incentive so as to encourage peers to offer resources (e.g, upload bandwidth) to the networks. In this paper, we consider fair bandwidth allocation of access links in P2P file-sharing networks and develop a coupled network-wide utility maximization model which aims at achieving several kinds of fairness among requesting peers. We provide a meaningful interpretation of the problem of maximizing social welfare and its sub-problems from an economic point of view. The coupled optimization problem is difficult to resolve in a distributed way because of its non-strict convexity and non-separation. We apply a modified successive approximation method to investigate the coupled problem and propose a distributed bandwidth allocation scheme to solve the approximation problems. Then, we investigate the convergence of the scheme by mathematical analysis and evaluate the performance through numerical examples, which validate that the scheme can achieve the global optimum within reasonable iterations.

2020, 16(3): 1119-1134 doi: 10.3934/jimo.2018195 +[Abstract](2041) +[HTML](823) +[PDF](445.39KB)
Abstract:

In this paper, in order to reduce possible packet loss of the primary users (PUs) in cognitive radio networks, we assume there is a buffer with a finite capacity for the PU packets. At the same time, focusing on the packet interruptions of the secondary users (SUs), we introduce a probability returning scheme for the interrupted SU packets. In order to evaluate the influence of the finite buffer setting and the probability returning scheme to the system performance, we construct and analyze a discrete-time Markov chain model. Accordingly, we determine the expressions of some important performance measures of the PU packets and the SU packets. Then, we show numerical results to evaluate how the buffer setting of the PU packets and the returning probability influence the system performance. Moreover, we optimize the system access actions of the SU packets. We determine their individually and the socially optimal strategies by considering different buffer settings for PU packets and different returning probabilities for SU packets. Finally, a pricing policy by introducing an admission fee is also provided to coincide the two optimal strategies.

2020, 16(3): 1135-1148 doi: 10.3934/jimo.2018196 +[Abstract](2336) +[HTML](831) +[PDF](693.89KB)
Abstract:

In this paper, we introduce a discrete time Geo/Geo/1 queue system with non-preemptive priority and multiple working vacations. We assume that there are two types of customers in this queue system named "Customers of type-Ⅰ" and "Customers of type-Ⅱ". Customer of type-Ⅱ has a higher priority with non-preemption than Customer of type-Ⅰ. By building a discrete time four-dimensional Markov Chain which includes the numbers of customers with different priorities in the system, the state of the server and the service state, we obtain the state transition probability matrix. Using a birth-and-death chain and matrix-geometric method, we deduce the average queue length, the average waiting time of the two types of customers, and the average busy period of the system. Then, we provide some numerical results to evaluate the effect of the parameters on the system performance. Finally, we develop some benefit functions to analyse both the personal and social benefit, and obtain some optimization results within a certain range.

2020, 16(3): 1149-1169 doi: 10.3934/jimo.2018197 +[Abstract](1742) +[HTML](826) +[PDF](760.54KB)
Abstract:

Channel reservation strategy in CRNs is an effective technology for conserving communication resources. In this paper, using the imperfect sensing of secondary user (SU) packets, and considering the patience degree of SU packets, we propose a channel reservation strategy in a CRN. Aligned with the proposed channel reservation strategy, we establish a continuous-time Markov chain model to capture the stochastic behavior of the two types of user packets. Then, in order to obtain the steady-state probability distribution for the system model, we present a new algorithm for solving the quasi-birth-and-death (QBD) process. At last, based on the energy detection method, we evaluate the system performance in terms of the throughput of SU packets, the average latency of SU packets, the switching rate of SU packets and the channel utilization in relation to the energy detection threshold and the number of reserved channels.

2020, 16(3): 1171-1185 doi: 10.3934/jimo.2018198 +[Abstract](2088) +[HTML](940) +[PDF](420.65KB)
Abstract:

In this paper, we provide a smoothing sample average approximation (SAA) method to solve a portfolio choice model based on second-order stochastic dominance (SSD) measure. Introducing a second-order stochastic dominance constraint in portfolio choice is theoretically attractive since all risk-averse investors would prefer a dominating portfolio. However, how to get the best choice among SSD efficient portfolios which is based on a stochastic optimization model is a challenge. We use the sample average to approximate the expected return rate function in the model and get a linear/nonlinear programming when the benchmark has discrete distribution. Then we propose a smoothing penalty algorithm to solve this problem. Meanwhile, we investigate the convergence of the optimal value of the transformed model and show that the optimal value converges to its counterpart with probability approaching to one at exponential rate as the sample size increases. By comparing the numerical results of the smoothing SAA algorithm with the common linear programming (LP) algorithm, we find that the smoothing algorithm has better performance than the LP algorithm in three aspects: (ⅰ)the smoothing SAA method can avoid the infinite constraints in the transformed models and the size of the smoothing algorithm model will not increase as the sample grows; (ⅱ)the smoothing SAA algorithm can deal with the nonlinear portfolio models with nonlinear transaction cost function; (ⅲ) the smoothing algorithm can get the global optimal solution because the smoothing function maintains the original convexity.

2020, 16(3): 1187-1202 doi: 10.3934/jimo.2018199 +[Abstract](2109) +[HTML](1005) +[PDF](585.73KB)
Abstract:

This paper considers an inventory mechanism in which the supplier may provide a short-term price discount to the retailer at a future time with some uncertainty. To maximize the retailer's profit in this setting, we establish an optimal replenishment and stocking strategy model. Based on the retailer's inventory cost-benefit analysis, we present a closed-form solution for the inventory model and provide an optimal ordering policy to the retailer. Numerical experiments and numerical sensitivity are given to provide some high insights to the inventory model.

2020, 16(3): 1203-1220 doi: 10.3934/jimo.2018200 +[Abstract](2555) +[HTML](1009) +[PDF](267.72KB)
Abstract:

Vehicle routing problem (VRP) is a typical and important combinatorial optimization problem, and is often involved with complicated temporal and spatial constraints in practice. In this paper, the VRP is formulated as an optimization model for minimizing the number of vehicles and the total transportation cost subject to constraints on loading plan, service time and weight capacity. The transportation cost consists of the rent charge of vehicles, fuel cost, and carbon tax. Owing to complexity of the built model, it is divided into two subproblems by a two-stage optimization approach: at the first stage, the number of vehicles is minimized, then the routing plan is optimized at the second stage. For solving the sequential subproblems, two correlated genetic algorithms are developed, which share the same initial population to reduce their computational costs. Numerical results indicate that the developed algorithms are efficient, and a number of important managerial insights are revealed from the model.

2020, 16(3): 1221-1233 doi: 10.3934/jimo.2018201 +[Abstract](1974) +[HTML](951) +[PDF](348.33KB)
Abstract:

The concepts of essential solutions and essential solution sets for generalized semi-infinite optimization problems (GSIO for brevity) are introduced under functional perturbations, and the relations among the concepts of essential solutions, essential solution sets and lower semicontinuity of solution mappings are discussed. We show that a solution is essential if and only if the solution is unique; and a solution subset is essential if and only if it is the solution set itself. Some sufficient conditions for the upper semicontinuity of solution mappings are obtained. Finally, we show that every GSIO problem can be arbitrarily approximated by stable GSIO problems (the solution mapping is continuous), i.e., the set of all stable GSIO problems is dense in the set of all GSIO problems with the given topology.

2020, 16(3): 1235-1259 doi: 10.3934/jimo.2018202 +[Abstract](2291) +[HTML](979) +[PDF](1287.03KB)
Abstract:

Integrated process planning and scheduling (IPPS) problems are one of the most important flexible planning functions for a job shop manufacturing. In a manufacturing order to produce n jobs (parts) on m machines in a flexible manufacturing environment, an IPPS system intends to generate the process plans for all n parts and the overall job-shop schedule concurrently, with the objective of optimizing a manufacturing objective such as make-span. The optimization of the process planning and scheduling will be applied through an integrated approach based on Fuzzy Inference System (FIS), to provide for flexibilities of the given components and consider the qualitative parameters. The FIS, Constraint Programming (CP) and Simulated Annealing (SA) algorithms are applied in this design. The objectives of the proposed model consist of maximization of processes utility, minimization of make-span and total production costs including costs of flexible tools, machines, process and TADs. The proposed approach indicates that The CP and SA algorithms are able to resolve the IPPS problem with multiple objective functions. The experiments and related results indicate that the CP method outperforms the SA algorithm.

2020, 16(3): 1261-1272 doi: 10.3934/jimo.2019001 +[Abstract](1821) +[HTML](720) +[PDF](369.35KB)
Abstract:

In this paper, the Clarke generalized Jacobian of the generalized regularized gap function for a nonmonotone Ky Fan inequality is studied. Then, based on the Clarke generalized Jacobian, we derive a global error bound for the nonmonotone Ky Fan inequalities. Finally, an application is given to provide a descent method.

2020, 16(3): 1273-1296 doi: 10.3934/jimo.2019002 +[Abstract](2262) +[HTML](896) +[PDF](554.12KB)
Abstract:

This study develops a single-machine manufacturing system for multi-product with defective items and delayed payment policy. Contradictory to the literature limited production capacity and partial backlogging are considered for more realistic result. The objective of this research is to obtain the optimal cycle length, optimal production quantity, and optimal backorder quantity of each product such that the expected total cost is minimum. The model is solved analytically. Three efficient lemmas are developed to obtain the global optimum solution of the model. An improved algorithm is designed to obtain the numerical solution of the model. An illustrative numerical example and sensitivity analysis are provided to show the practical usage of proposed method.

2020, 16(3): 1297-1310 doi: 10.3934/jimo.2019003 +[Abstract](1937) +[HTML](1093) +[PDF](404.42KB)
Abstract:

A discrete variant of a multicriteria investment portfolio optimization problem with Savage's risk criteria is considered. One of the three problem parameter spaces is endowed with Hölder's norm, and the other two are endowed with Chebyshev's norm. The lower and upper attainable bounds on the stability radius of one Pareto optimal portfolio are obtained. We illustrate the application of our theoretical results by modeling a relevant case study.

2020, 16(3): 1311-1328 doi: 10.3934/jimo.2019004 +[Abstract](1352) +[HTML](668) +[PDF](432.7KB)
Abstract:

This paper extends the multidimensional credibility model under balanced loss function to account for not only certain conditional dependence over time for claim amounts but also dependence across individual risks and over portfolio risks. By means of orthogonal projection method in Hilbert space of random vectors, the inhomogeneous and homogeneous multidimensional credibility estimators are derived, which generalize some well known existing results in credibility theory. Moreover, the unbiased estimators of structural parameters are investigated. Finally, we present a numerical example to show the existence of the multidimensional credibility estimators and their difference from the existing ones.

2020, 16(3): 1329-1347 doi: 10.3934/jimo.2019005 +[Abstract](1666) +[HTML](807) +[PDF](1049.38KB)
Abstract:

In this paper, we consider due-date related single machine scheduling problems, where two agents compete for utilizing a common processing resource (i.e. a single machine). In this paper, we provide a detailed and a systemic literature review of the two-agent scheduling problem dealing with models with a given due date. We consider the following four main cases: 1) the earliness and tardiness, 2) the maximum lateness, 3) the number of tardy jobs and 4) the late work criteria. To do so, we classify due-date related, two-agent scheduling problems into two categories on the basis of the objective function setting, (i.e. the feasibility model and the minimality model). The feasibility model minimizes the objective function of one agent subject to an upper bound on the objective for the other agent. The minimality model assigns certain weights for two agents and as a result minimizes their weighted objectives. In the present paper, we list the computational complexities and proposed algorithms for the due-date related, two-agent scheduling problem, investigated in the literature since 2003.

2020, 16(3): 1349-1368 doi: 10.3934/jimo.2019006 +[Abstract](1852) +[HTML](746) +[PDF](2593.86KB)
Abstract:

In this work we develop partial differential equation (PDE) based computational models for pricing real options to contract the production or to transfer part/all of the ownership of a project when the underlying asset price of the project satisfies a geometric Brownian motion. The developed models are similar to the Black-Scholes equation for valuing conventional European put options or the partial differential linear complementarity problem (LCP) for pricing American put options. A finite volume method is used for the discretization of the PDE models and a penalty approach is applied to the discretized LCP. We show that the coefficient matrix of the discretized systems is a positive-definite \begin{document}$M$\end{document}-matrix which guarantees that the solution from the penalty equation converges to that of the discretized LCP. Numerical experiments, performed to demonstrate the usefulness of our methods, show that our models and numerical methods are able to produce financially meaningful numerical results for the two non-trivial test problems.

2020, 16(3): 1369-1388 doi: 10.3934/jimo.2019007 +[Abstract](1777) +[HTML](721) +[PDF](474.83KB)
Abstract:

We consider the equilibrium and socially optimal behavior of strategic customers in a discrete-time queue with bulk service. The service batch size varies from a single customer to a maximum of 'b' customers. We study the equilibrium and socially optimal balking strategies under two information policies: observable and unobservable. In the former policy, a service provider discloses the queue length information to arriving customers and conceals it in the latter policy. The effect of service batch size and other queueing parameters on the equilibrium strategies under both information policies are compared and illustrated with numerical experiments.

2020, 16(3): 1389-1414 doi: 10.3934/jimo.2019008 +[Abstract](2696) +[HTML](936) +[PDF](471.81KB)
Abstract:

This paper studies an original equipment manufacturer's (OEM's) optimal production and pricing decisions and the governments optimal subsidy level when the number of used products returning to the OEM is uncertain. The government aims to minimize its total expenditures but also attempt to achieve a given target collection level. We model the problem as an extended price-setting newsvendor model, which simultaneously incorporates supply uncertainty and external government influence. Moreover, we consider separately the cases of stochastic supplies with additive and multiplicative return uncertainty. We show that under the above settings, the governments optimal strategy is to provide only sufficient subsidies that cause its target to be met exactly. The government subsidies will mitigate the cost of remanufacturing and increase the total collection efforts of the government and the manufacturer. Moreover, the return uncertainty lowers both the manufacturers profits and selling price, whereas its effects on the governments optimal subsidies and the manufacturers optimal return efforts are insignificant. Therefore, the manufacturer is worse off but consumers are better off under the conditions of uncertain returns. By comparing the optimal decisions when the government is a central planner with the case of decentralized decision making, or comparing the arrangement in which the government provides subsidies directly to the manufacturer rather than to consumers, we find that the government subsidies would coordinate the supply chain only when its target collection level is high. Moreover, no essential differences exist between providing subsidies directly to the manufacturer and to consumers. Our results are robust under both the additive and multiplicative uncertainty models.

2020, 16(3): 1415-1433 doi: 10.3934/jimo.2019009 +[Abstract](1808) +[HTML](711) +[PDF](607.38KB)
Abstract:

In this paper, an \begin{document}$(s, S)$\end{document} continuous inventory model with perishable items and retrial demands is proposed. In addition, replenishment lead times that are independent and identically distributed according to phase-type distribution are implemented. The proposed system is modeled as a three-dimensional Markov process using a level-dependent quasi-birth-death (QBD) process. The ergodicity of the modeled Markov system is demonstrated and the best method for efficiently approximating the steady-state distribution at the inventory level is determined. This paper also provides performance measure formulas based on the steady-state distribution of the proposed approximation method. Furthermore, in order to minimize the system cost, the optimum values of \begin{document}$s$\end{document} and \begin{document}$S$\end{document} are determined numerically and sensitivity analysis is performed on the main parameters.

2020, 16(3): 1435-1456 doi: 10.3934/jimo.2019010 +[Abstract](1731) +[HTML](704) +[PDF](477.06KB)
Abstract:

We consider the dynamic lot size problem for perishable inventory under minimum order quantities. The stock deterioration rates and inventory costs depend on both the age of the stocks and their periods of order. Based on two structural properties of the optimal solution, we develop a dynamic programming algorithm to solve the problem without backlogging. We also extend the model by considering backlogging. By establishing the regeneration set, we give a sufficient condition for obtaining forecast horizon under without and with backlogging. Finally, based on a detailed test bed of instance, we obtain useful managerial insights on the impact of minimum order quantities and perishability of product and the costs on the length of forecast horizon.

2020, 16(3): 1457-1479 doi: 10.3934/jimo.2019011 +[Abstract](1800) +[HTML](719) +[PDF](477.48KB)
Abstract:

This paper investigates an optimal reinsurance-investment problem in relation to thinning dependent risks. The insurer's wealth process is described by a risk model with two dependent classes of insurance business. The insurer is allowed to purchase reinsurance and invest in one risk-free asset and one risky asset whose price follows CEV model. Our aim is to maximize the expected exponential utility of terminal wealth. Applying Legendre transform-dual technique along with stochastic control theory, we obtain the closed-form expression of optimal strategy. In addition, our wealth process will reduce to the classical Cramér-Lundberg (C-L) model when \begin{document}$p = 0$\end{document}, in this case, we achieve the explicit expression of the optimal strategy for Hyperbolic Absolute Risk Aversion (HARA) utility by using Legendre transform. Finally, some numerical examples are presented to illustrate the impact of our model parameters (e.g., interest and volatility) on the optimal reinsurance-investment strategy.

2020, 16(3): 1481-1502 doi: 10.3934/jimo.2019012 +[Abstract](2931) +[HTML](888) +[PDF](457.87KB)
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In this paper, a numerical method based on least squares support vector machines has been developed to solve the initial and boundary value problems of higher order nonlinear ordinary differential equations. The numerical experiments have been performed on some nonlinear ordinary differential equations to validate the accuracy and reliability of our proposed LS–SVM model. Compared with the exact solution, the results obtained by our proposed LS–SVM model can achieve a very high accuracy. The proposed LS–SVM model could be a good tool for solving higher order nonlinear ordinary differential equations.

2020, 16(3): 1503-1518 doi: 10.3934/jimo.2019013 +[Abstract](1751) +[HTML](712) +[PDF](429.34KB)
Abstract:

This paper proposes a new class of accelerated conjugate-gradient-like algorithms for solving large scale unconstrained optimization problems, which combine the idea of accelerated adaptive Perry conjugate gradient algorithms proposed by Andrei (2017) with the modified secant condition and the nonmonotone line search technique. An attractive property of the proposed methods is that the search direction always provides sufficient descent step which is independent of the line search used and the convexity of objective function. Under common assumptions, it is proven that the proposed methods possess global convergence for nonconvex smooth functions, and R-linear convergence for uniformly convex functions. The numerical experiments show the efficiency of the proposed method in practical computations.

2020, 16(3): 1519-1526 doi: 10.3934/jimo.2019014 +[Abstract](1758) +[HTML](710) +[PDF](361.84KB)
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We establish a theoretical framework for the problem of phaseless compressed sensing with partially known signal support, which aims at generalizing the Null Space Property and the Strong Restricted Isometry Property from phase retrieval to partially sparse phase retrieval. We first introduce the concepts of the Partial Null Space Property (P-NSP) and the Partial Strong Restricted Isometry Property (P-SRIP); and then show that both the P-NSP and the P-SRIP are exact recovery conditions for the problem of partially sparse phase retrieval. We also prove that a random Gaussian matrix \begin{document}$A\in \mathbb{R}^{m\times n}$\end{document} satisfies the P-SRIP with high probability when \begin{document}$m = O(t(k-r)\log(\frac{n-r}{t(k-r)})).$\end{document}

2020, 16(3): 1527-1538 doi: 10.3934/jimo.2019015 +[Abstract](1680) +[HTML](648) +[PDF](370.37KB)
Abstract:

The parameters in the semidefinite programming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical properties of estimates of the optimal value and the optimal solutions are given in this paper, when the estimated parameters are both in the objective function and in the constraints. This analysis is mainly based on the theory of the linear programming and the perturbation theory of the semidefinite programming.

2020, 16(3): 1539-1553 doi: 10.3934/jimo.2019016 +[Abstract](1939) +[HTML](928) +[PDF](835.74KB)
Abstract:

At the peak of a service system, customers may hesitate and even leave in the face of unavoidable queuing. This phenomenon not only affects the customer's satisfaction, but also causes the loss of the company's revenue. This paper establishes a fluid model of customer queuing behavior for the customer losses. The goal is to reduce the customer losses, and the setting and optimization method of quick queue in random service systems is studied. We construct two queuing models, in which one includes only regular queues and the other includes both regular and quick queues. We analyze the queuing systems, and describe the different forms of the objective function based on the fluid model of customer behavior. Then we compare and analyze the impact of the adoption of quick queues on the performance of the service system during peak period, and design a calculation method to obtain the optimal value for setting the number of quick queues. Thus, the overall performance of the system is optimized. Finally, we take the setting and optimization of quick queue in the supermarket service system as an example, which verifies the validity of the proposed method, and shows the reference value of this method to management practice.

2019  Impact Factor: 1.366